card marked with the number 2 to 101 are placed in a box and mixed tho

1.	card marked with the number 2 to 101 are placed in a box and mixed thoroughly. One card is drown from this box , find the probability that tha number of the card is . (a) an even number , (b) a number less then 14. , (c) a number which is a perfect square. , (d) a prime number less then 20.
Answer» $\large\underline{\bold{Given- }}$ Card marked with the number 2 to 101 are placed in a box. One card is taken out randomly from the box. $\large\underline{\sf{To\:Find - }}$ (a) an even number (B) a number less than 14 (c) a number which is a perfect square (d) a prime number less than 20. $\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$ $\sf \:<klux>PROBABILITY</klux> \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$ $\large\underline{\sf{Solution-}}$ Given that Cards number from 2 to 100 are in the box, it implies, there are 100 cards in the box and one card can be taken out in 100 ways. So, total number of outcomes = 100. $\large\underline{\sf{Answer (a)- }}$ From 2 to 101, The even numbers are 2, 4, 6, _ _ _ _, 100. It implies, there are 50 even numbers. So, Total number of favourable outcomes are 50. Hence, $\sf \:Probability \: of \: getting \: even \: number =\dfrac{50}{100} = \dfrac{1}{2}$ $\large\underline{\sf{Answer (b)- }}$ From 2 to 101, Cards bearing number less than 14 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. It implies, there are 12 cards bearing number less than 14. So, Total number of favourable outcomes are 12. Thus, $\sf \:Probability \: of \: getting \: \: number \: < 14 =\dfrac{12}{100} = \dfrac{3}{25}$ $\large\underline{\sf{Answer (c)- }}$ From 2 to 101, the numbers which are perfect squares are 4, 9, 16, 25, 36, 49, 64, 81, 100 It means these are squares of 9 cards having number 2, 3, 4, 5, 6, 7, 8, 9, 10 So, Total number of favourable outcomes are 9. Hence, $\sf \:Probability \: of \: getting \: perfect \: square \: number =\dfrac{9}{100}$ $\large\underline{\sf{Answer (d)- }}$ From 2 to 101, prime number less than 20 are 2, 3, 5, 7, 11, 13, 17, 19. It implies, there are 8 prime numbers less than 20 So, Total number of favourable outcomes are 8. Thus, $\sf \:Probability \: of \: getting \:prime \: number < 20=\dfrac{8}{100} = \dfrac{2}{25}$ Additional Information :- Explore more :- The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any OUTCOME is a number between 0 and 1. The probability of sure event is 1. The probability of impossible event is 0. The probabilities of all the outcomes ADD up to 1. The probability of any event A is the sum of the probabilities of the outcomes in A.

card marked with the number 2 to 101 are placed in a box and mixed thoroughly. One card is drown from this box , find the probability that tha number of the card is . (a) an even number , (b) a number less then 14. , (c) a number which is a perfect square. , (d) a prime number less then 20.

Answer»

$\large\underline{\bold{Given- }}$

Card marked with the number 2 to 101 are placed in a box.

One card is taken out randomly from the box.

$\large\underline{\sf{To\:Find - }}$

(a) an even number

(B) a number less than 14

(d) a prime number less than 20.

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$

$\sf \:<klux>PROBABILITY</klux> \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

$\large\underline{\sf{Solution-}}$

Given that

Cards number from 2 to 100 are in the box,

it implies, there are 100 cards in the box and one card can be taken out in 100 ways.

So, total number of outcomes = 100.

$\large\underline{\sf{Answer (a)- }}$

From 2 to 101,

The even numbers are 2, 4, 6, _ _ _ _, 100.

It implies, there are 50 even numbers.

So,

Total number of favourable outcomes are 50.

Hence,

$\sf \:Probability \: of \: getting \: even \: number =\dfrac{50}{100} = \dfrac{1}{2}$

$\large\underline{\sf{Answer (b)- }}$

From 2 to 101,

Cards bearing number less than 14 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

It implies, there are 12 cards bearing number less than 14.

So,

Total number of favourable outcomes are 12.

Thus,

$\sf \:Probability \: of \: getting \: \: number \: < 14 =\dfrac{12}{100} = \dfrac{3}{25}$

$\large\underline{\sf{Answer (c)- }}$

From 2 to 101, the numbers which are perfect squares are 4, 9, 16, 25, 36, 49, 64, 81, 100

It means these are squares of 9 cards having number 2, 3, 4, 5, 6, 7, 8, 9, 10

So,

Total number of favourable outcomes are 9.

Hence,

$\sf \:Probability \: of \: getting \: perfect \: square \: number =\dfrac{9}{100}$

$\large\underline{\sf{Answer (d)- }}$

From 2 to 101, prime number less than 20 are 2, 3, 5, 7, 11, 13, 17, 19.

It implies, there are 8 prime numbers less than 20

So,

Total number of favourable outcomes are 8.

Thus,

$\sf \:Probability \: of \: getting \:prime \: number < 20=\dfrac{8}{100} = \dfrac{2}{25}$

Additional Information :-

Explore more :-

The sample space of a random experiment is the collection of all possible outcomes.

An event associated with a random experiment is a subset of the sample space.

The probability of any OUTCOME is a number between 0 and 1.

The probability of sure event is 1.

The probability of impossible event is 0.

The probabilities of all the outcomes ADD up to 1.

The probability of any event A is the sum of the probabilities of the outcomes in A.